What is the problem with a crane motor if it cannot lift a load and makes a heavy humming sound?

It sounds like the motor stalled and the rotor was locked. In this state there is a heavy current draw that can burn the motor out. Hopefully it is protected by overload protection and the heaters should have taken the motor off line. The motor and crane should have been matched together as a unit. Check the mechanical capacity of the crane to make sure that it isn't working outside its lifting capacity. If the crane has a mechanical break on it check and make sure that the break is releasing when the motor starts.